Boundary Shape and Casimir Energy

Casimir energy changes are investigated for geometries obtained by small but arbitrary deformations of a given geometry for which the vacuum energy is already known for the massless scalar field. As a specific case, deformation of a spherical shell is studied. From the deformation of the sphere we show that the Casimir energy is a decreasing function of the surface to volume ratio. The decreasing rate is higher for less smooth deformations.Comment: 12 page

Single scale factor for the universe from the creation of radiation and matter till the present

A scheme for incorporating the creation of radiation and matter into the cosmological evolution is introduced so that it becomes possible to merge the times before and after the creation of radiation and matter in a single scale factor in Robertson-Walker metric. This scheme is illustrated through a toy model that has the prospect of constituting a basis for a realistic model.Comment: Minor typos are corrected, an acknowledgment is added, to be published in The European Physical Journal

Higgsed Stueckelberg Vector and Higgs Quadratic Divergence

Here we show that, a hidden vector field whose gauge invariance is ensured by a Stueckelberg scalar and whose mass is spontaneously generated by the Standard Model Higgs field contributes to quadratic divergences in the Higgs boson mass squared, and even leads to its cancellation at one-loop when Higgs coupling to gauge field is fine-tuned. In contrast to mechanisms based on hidden scalars where a complete cancellation cannot be achieved, stabilization here is complete in that the hidden vector and the accompanying Stueckelberg scalar are both free from quadratic divergences at one-loop. This stability, deriving from hidden exact gauge invariance, can have important implications for modelling dark phenomena like dark matter, dark energy, dark photon and neutrino masses. The hidden fields can be produced at the LHC.Comment: 5pp, 1 fig. Improved exposition, rectified concurrency to broken and unbroken electroweak vacua, added reference

Finite-parameter feedback control for stabilizing the complex Ginzburg-Landau equation

In this paper, we prove the exponential stabilization of solutions for complex Ginzburg-Landau equations using finite-parameter feedback control algorithms, which employ finitely many volume elements, Fourier modes or nodal observables (controllers). We also propose a feedback control for steering solutions of the Ginzburg-Landau equation to a desired solution of the non-controlled system. In this latter problem, the feedback controller also involves the measurement of the solution to the non-controlled system.Comment: 20 page

Directed Growth of Hydrogen Lines on Graphene: High Throughput Simulations Powered by Evolutionary Algorithm

We set up an evolutionary algorithm combined with density functional tight-binding (DFTB) calculations to investigate hydrogen adsorption on flat graphene and graphene monolayers curved over substrate steps. During the evolution, candidates for the new generations are created by adsorption of an additional hydrogen atom to the stable configurations of the previous generation, where a mutation mechanism is also incorporated. Afterwards a two-stage selection procedure is employed. Selected candidates act as the parents of the next generation. In curved graphene, the evolution follows a similar path except for a new mechanism, which aligns hydrogen atoms on the line of minimum curvature. The mechanism is due to the increased chemical reactivity of graphene along the minimum radius of curvature line (MRCL) and to sp$^3$ bond angles being commensurate with the kinked geometry of hydrogenated graphene at the substrate edge. As a result, the reaction barrier is reduced considerably along the MRCL, and hydrogenation continues like a mechanical chain reaction. This growth mechanism enables lines of hydrogen atoms along the MRCL, which has the potential to overcome substrate or rippling effects and could make it possible to define edges or nanoribbons without actually cutting the material.Comment: 10 pages of main text, 37 pages of supplementary information, 1 supplementary vide

Characteristic Energy of the Coulomb Interactions and the Pileup of States

Tunneling data on $\mathrm{La_{1.28}Sr_{1.72}Mn_2O_7}$ crystals confirm Coulomb interaction effects through the $\sqrt{\mathrm{E}}$ dependence of the density of states. Importantly, the data and analysis at high energy, E, show a pileup of states: most of the states removed from near the Fermi level are found between ~40 and 130 meV, from which we infer the possibility of universal behavior. The agreement of our tunneling data with recent photoemission results further confirms our analysis.Comment: 4 pages, 4 figures, submitted to PR

Tevatron Higgs Mass Bounds: Projecting U(1)' Models to LHC Domain

We study Higgs boson masses in supersymmetric models with an extra U(1) symmetry to be called U(1)$^{\prime}$. Such extra gauge symmetries are urged by the $\mu$ problem of the MSSM, and they also arise frequently in low-energy supersymmetric models stemming from GUTs and strings. We analyze mass of the lightest Higgs boson and various other particle masses and couplings by taking into account the LEP bounds as well as the recent bounds from Tevatron experiments. We find that the $\mu$-problem motivated generic low-energy U(1)$^{\prime}$ model yields Higgs masses as large as $\sim 200\ {\rm GeV}$ and violate the Tevatron bounds for certain ranges of parameters. We analyze correlations among various model parameters, and determine excluded regions by both scanning the parameter space and by examining certain likely parameter values. We also make educated projections for LHC measurements in light of the Tevatron restrictions on the parameter space. We further analyze certain benchmark models stemming from E(6) breaking, and find that they elevate Higgs boson mass into Tevatron's forbidden band when U(1)$^{\prime}$ gauge coupling takes larger values than the one corresponding to one-step GUT breaking.Comment: 11 pages, 3 figure

Semi-classical black holes with large N re-scaling and information loss problem

We consider semi-classical black holes and related re-scalings with N massless fields. For a given semi-classical solution of an N = 1 universe, we can find other solution of a large N universe by the re-scaling. After the re-scaling, any curvature quantity takes a sufficiently small value without changing its causal structure. Via the re-scaling, we argue that black hole complementarity for semi-classical black holes cannot provide a fundamental resolution of the information loss problem, and the violation of black hole complementarity requires sufficiently reasonable amounts of N. Such N might be realized from some string inspired models. Finally, we claim that any fundamental resolution of the information loss problem should resolve the problem of the singularity.Comment: 33 pages, 5 figure

Higher Curvature Quantum Gravity and Large Extra Dimensions

We discuss effective interactions among brane matter induced by modifications of higher dimensional Einstein gravity via the replacement of Einstein-Hilbert term with a generic function f(R) of the curvature scalar R. After deriving the graviton propagator, we analyze impact of virtual graviton exchanges on particle interactions, and conclude that f(R) gravity effects are best probed by high-energy processes involving massive gauge bosons, heavy fermions or the Higgs boson. We perform a comparative analysis of the predictions of f(R) gravity and of Arkani-Hamed-Dvali-Dimopoulos (ADD) scenario, and find that the former competes with the latter when f''(0) is positive and comparable to the fundamental scale of gravity in higher dimensions. In addition, we briefly discuss graviton emission from the brane as well as its decays into brane-localized matter, and find that they hardly compete with the ADD expectations. Possible existence of higher-curvature gravitational interactions in large extra spatial dimensions opens up various signatures to be confronted with existing and future collider experiments.Comment: 19 pp, 2 figs. Added references, corrected typo

LEP Indications for Two Light Higgs Bosons and U(1)' Model

Reanalyses of LEP data have shown preference to two light CP-even Higgs bosons. We discuss implications of such a Higgs boson spectrum for the minimal supersymmetric model extended by a Standard Model singlet chiral superfield and an additional Abelian gauge invariance (the U(1)' model). We, in particular, determine parameter regions that lead to two light CP-even Higgs bosons while satisfying existing bounds on the mass and mixings of the extra vector boson. In these parameter regions, the pseudoscalar Higgs is found to be nearly degenerate in mass with either the lightest or next-to-lightest Higgs boson. Certain parameters of the U(1)' model such as the effective mu parameter are found to be significantly bounded by the LEP two-light-Higgs signal.Comment: 20 pp, 7 figs, 2 table